Ideal Gas Expansion - Finding final pressure and work done by gas

1. The problem statement, all variables and given/known data
a ideal monoatomic gas initally has a temperature of 315K and a pressure of 6.87atm . It then expands from a volume of 440cm^3 to volume 1550cm^3 .

If the expansion is isothermal, what is (A) the final pressure (in atm's) and (B) the work done by he gas.

2. Relevant equations
[itex]PV^{\gamma}=[/itex] constant

3. The attempt at a solution
For the final pressure I just did the following, no idea if this is correct mind you.

Extremely new to this material and have not got my head around the material yet, so I would be suprised if this is correct. The value does seem rather low. What I am a little concerned with is the fact they explicitly state the temperature of the gas, but I have not used temperature in any of the equations/formulas used. The question does go on further to ask for the final volume and work if the process was adiabatic rather than isothermal, so it may be used there?

EDIT: Just realised a school boy error with the integration. Have gone back and already amended it as of now.

1. The problem statement, all variables and given/known data
a ideal monoatomic gas initally has a temperature of 315K and a pressure of 6.87atm . It then expands from a volume of 440cm^3 to volume 1550cm^3 .

If the expansion is isothermal, what is (A) the final pressure (in atm's) and (B) the work done by he gas.

2. Relevant equations
[itex]PV^{\gamma}=[/itex] constant

.

Bad start. That's the p-V relationship for a reversible adiabatic process, not an isothermal one.

Bad start. That's the p-V relationship for a reversible adiabatic process, not an isothermal one.

Ah right ok, thanks. The question I posted up is Parts A and B. However, there is also a part C and D where it asks what the final pressure and work would be if it were an Adiabatic process instead. So it would be good to know if I have done that bit correct?

For isothermal expansion, is it simply [itex]PV=nRT[/itex] that would/could be used?

Ah right ok, thanks. The question I posted up is Parts A and B. However, there is also a part C and D where it asks what the final pressure and work would be if it were an Adiabatic process instead. So it would be good to know if I have done that bit correct?

Then you omitted a bunch of dV's in your integrals and you did not evaluate ∫V-γdV correctly. I haven't seen your emendation.

Also, be aware that in addition to being adiabatic the process also has to be quasi-static. (It is sufficient but not necessary for it to be reversible).

For isothermal expansion, is it simply [itex]PV=nRT[/itex] that would/could be used?

Then you omitted a bunch of dV's in your integrals and you did not evaluate ∫V-γdV correctly. I haven't seen your emendation.

Also, be aware that in addition to being adiabatic the process also has to be quasi-static. (It is sufficient but not necessary for it to be reversible).

Yes.

Ok thanks. For parts D and C it just says if it were an Adiabatic process instead, it doesnt state anything else about it being reversible etc, will that make a difference? If I could change the OP and amend it to say Adiabatic rather than Isothermal I would, as I think that is the one I need more help with, so lets carry on with that one. I will try and amed the integration now below (as I can no longer edit the OP). Also apologies for forgetting some of the dV's, as I am (relatively) new to integration it is something I sometimes forget, in my OP where I stated I went back to amend an error, I did, but obviously not every error, just the one I could see; I just double checked something on my calculator and do not know what happened last night but I can see where I went wrong, I added 1 to 7/5 , not -7/5.

How many cc's in 1 cubic meter? Not 1000. Otherwise looks OK. (Except why your prof wants you to use an incorrect value for monatomic gas gamma is beyond me ... )

Then for the work done i have amended the integration, without putting values in. Just to see if the integration itself is correct.
('c' is the constant that [itex]P_iV_i^{\gamma}[/itex] and [itex]P_fV_f^{\gamma}[/itex] are equal to.

EDIT: oh I see you quoted before I amended something in my post, I forgot the minus signs but put them in now.

I think you've got it now.

You should discuss the requirement of quasi-staticity in adiabatic processes, without which pv to the gamma = constant is invalid.

For example, a free expansion of gas in an insulated box (gas is initially on one side, then is allowed to expand to full extent of box) is adiabatic (no heat in or out) but is not quasi-static and therefore you can't use pv to the gamma = constant.

You should discuss the requirement of quasi-staticity in adiabatic processes, without which pv to the gamma = constant is invalid.

For example, a free expansion of gas in an insulated box (gas is initially on one side, then is allowed to expand to full extent of box) is adiabatic (no heat in or out) but is not quasi-static and therefore you can't use pv to the gamma = constant.

Ok, many thanks for your help. My lecturer did say to use 7/5 for gamma, is that a wrong value to use in this case?

If the piston is expanding what will be the sign of pdV? What's the sign of p? of dV?

The question doesnt state anything about a piston though, or is it the same for all cases? The pressure would decrease, if like in this case the volume is increased, so would P be negative? dV would be positive, so therefore PdV would be negative? If its that easy, I did not know you could treat the differentials like normal.

I think I have done it correct then. But the reason I asked was because I have had a go at the first two parts, regarding the final pressure and work done in the isothermal case, and using [itex]PV=nRT[/itex], I got the final pressure fine but then my final answer for the work done is a positive value, so does that mean it is definitely wrong?

The question doesnt state anything about a piston though, or is it the same for all cases? The pressure would decrease, if like in this case the volume is increased, so would P be negative? dV would be positive, so therefore PdV would be negative? If its that easy, I did not know you could treat the differentials like normal.

p may be decreasing but it's still positive. No such thing as negative pressure in a gas.
work = ∑ pdV = ∫pdV. p is +, dV is +, so W is +.

I think I have done it correct then. But the reason I asked was because I have had a go at the first two parts, regarding the final pressure and work done in the isothermal case, and using [itex]PV=nRT[/itex], I got the final pressure fine but then my final answer for the work done is a positive value, so does that mean it is definitely wrong?[/QUOTE]
as I said , W is +.